Like their predecessors, handwritten numerical notations develop from, and thus reflect, the capabilities and properties of the technologies that preceded them, things like fingers, tallies, and tokens (Table 7.1). Thus, notations both accumulate and group, not because of some kind of innate predisposition for a concept of number with these qualities, but rather, because the material devices that preceded them accumulated and grouped. Like each of their precursors did, notations also respond to the limitations of their predecessors, for example, by providing the persistence in recording that manipulable forms cannot. Notations also bring new capabilities and limitations to the cognitive system for numbers, for example, adding conciseness and being fixed rather than manipulable. Their conciseness lets notations represent numbers at an unprecedented volume, enabling the compilation of tables of relations that influence numbers toward being conceived of in terms of their relations; their fixedness motivates the development of algorithms based on the knowledge of numerical relations, rather than the physical movements of elements like beads on an abacus. In sum, notations are part of the chronology of material forms for numbers, albeit the last to emerge and most elaborated form known. As such, numerical notations share a continuity of descent with precursors like tokens, tallies, and fingers.